Question

xYZ Candy makes specialty chocolate bars to distribute online, shipping across North America. XYZ has established a great deal of monopoly power in pricing given its specialty status. Let’s assume XYZ’s customers are identical with individual (inverse) demand as P = 2.50 – 0.1Q, where Q is number of bars the customer orders per month. Marginal cost to supply another bar is constant (equal to average cost) at $0.50. If XWZ acts like a single-price non-discriminating monopoly, its profit-maximizing price is $1.50 and quantity is 10 (you can check this!)

a. Suppose XYZ offers a quantity discount where it sells customers the first 10 units at $1.50 each but discounts the price for each bar ordered over 10 units (i.e., a lower price for the 11th bar and all beyond that). What will be the discounted price that maximizes profit? (Hint: The relevant portion of the demand curve for the discount pricing are quantities beyond price $1.50 and 10 units; it may help to think of this portion of the demand curve as a new demand curve beginning with the 11th unit, or a shift in the demand of 10 units for price $1.50 or below.)

b. How many bars does XYZ sell at the discounted price?

c. Compare the profit in the discounted pricing scheme to the monopoly single price of $1.50.

d. Suppose XYZ adds a three-tier pricing policy. Explain what would happen to profits.

e. Explain what happens to consumer surplus as XYZ adds more discount pric

Answer 1

a) Relevant portion of the demand curve for discount pricing is P= 2.50 - 0.1(Q - 10) = 1.5 - 0.1Q or P= 1.5 - 0.1Q

Profit obtained from discount pricing = Revenue - Cost = PQ - average cost*Q = (1.5 - 0.1Q)Q - 0.5Q = Q - 0.1Q^​​​2

First order Condition of profit maximisation is d(profit)/dq = 0

d(Q - 0.1Q^​​​2)/dQ = 0 or 1-0.2Q = 0 or Q = 5 bars

Price = 1.5 - 0.1*5 =1 . Price is $1

b) 5 bars are sold at discounted price $1 .In total 10+5 = 15 bars wede sold.

c) Profit at price $1.5 = P*Q - average cost*Q = 1.5*10 - 0.5*10 = $10

Profit at discounted price = P*Q - average cost*Q = 1*5 - 0.5*5 = $2.5

$2.5 is additional profit which discriminatory monopolist sells when he offers discounted price. In total when monopolist offers discounted profit , profit he earns in total is $(10+2.5) = $12.5

d) lets us see what would happen if monopolist offers three layer pricing and he sets third price such that he gains maximum profit from remaining portion of demand curve.

Relevant portion of demand curve : P= 2.5 - 0.1*(Q - 10-5) or P= 1 - 0.1Q

Profit = P*Q - average cost* Q = (1 - 0.1Q)Q - 0.5Q = 0.5Q - 0.1Q^​​​2

First order Condition of profit maximisation d(profit)/dQ = 0 or 0.5 - 0.2Q = 0 or Q = 2.5 units.

P= 1- 0.1*2.5 = $0.75

Profit = 0.75*2.5 - 0.5*2.5 = 0.25*2.5 = $0.625

We find that monopolist's profit further increases by $0.625 in three layer pricing.

e)

This is the case of second degree price discrimination in monopoly. The purpose of price discrimination is to capture the consumer surplus.

A monopolist cannot decrease the overall price from P= $1.5 to capture additional demand because then that would led to decrease in price for all the units he sells . Therefore he comes with a policy of price layering.

At discounted price Consumer is definitely able to consume additional good , consumer surplus does increases for him even in this case. But a part, in fig 1, it is shown by square abcd , is captured by the monopolist. If the monopolist decreased the price to $1, rather than offering discount price policy, abcd would have been the consumer surplus.

00 Price (3) P=105 a a To 10 15 quantity